Answer
$t = 1.5~s$
Work Step by Step
Initially, all the current will flow through the fuse and no current will flow through the resistor.
To find $t$, we can rewrite Equation (30-39) assuming that $R = 0$:
$L~\frac{di}{dt} = \mathscr{E}$
$\frac{di}{dt} = \frac{\mathscr{E}}{L}$
$i = \frac{\mathscr{E}}{L}~t$
$t = \frac{i~L}{\mathscr{E}}$
$t = \frac{(3.0~A)(5.0~H)}{10~V}$
$t = 1.5~s$
